# Problem

• Jun 3rd 2006, 06:01 PM
Nichelle14
Problem
I don't know if any one can help, but here it goes:

Here how the problem starts: The fundamental theroem of calculus was proved by showing that by a clever choice of the sample points for a Riemann sum, you can geta a value for Rsubn that is independent of n, no matter how large n is. The same reasoning can be used to fidn a Riemann sum with n =1 increment.

Then I have two graphs. First is a graph of f(x) = 3x^2, and g(x) = integral of f(x)dx (with C = 0). ( These two functions are graphed) ( I don't know how to show graphs on here. IF anyone knows can you tell me?)

here are the questions:
a. On the graph, illustrate the point x=c in (1,3) where the conclusion of the mean value theorem is true for g on the interval [1,3]. Then calculate the value of c. I did this and got the answer 13.

b. On the f graph, show a Riemann "sum" with one rectangel, using the x = c from part a as the sample point. Then calculate the value of the Riemann "sum". I wasn't too sure how to do this one.